This adapter can be used to wrap functions subject to simple bounds on
parameters so they can be used by optimizers that do not directly
support simple bounds.

The principle is that the user function that will be wrapped will see its
parameters bounded as required, i.e when its value method is called
with argument array point, the elements array will fulfill requirement
lower[i] <= point[i] <= upper[i] for all i. Some of the components
may be unbounded or bounded only on one side if the corresponding bound is
set to an infinite value. The optimizer will not manage the user function by
itself, but it will handle this adapter and it is this adapter that will take
care the bounds are fulfilled. The adapter value(double[]) method will
be called by the optimizer with unbound parameters, and the adapter will check
if the parameters is within range or not. If it is in range, then the underlying
user function will be called, and if it is not the value of a penalty function
will be returned instead.

This adapter is only a poor man solution to simple bounds optimization constraints
that can be used with simple optimizers like SimplexOptimizer with NelderMeadSimplex or MultiDirectionalSimplex. A better solution is to use
an optimizer that directly supports simple bounds like CMAESOptimizer or
BOBYQAOptimizer. One caveat of this poor man solution is that if start point
or start simplex is completely outside of the allowed range, only the penalty function
is used, and the optimizer may converge without ever entering the range.

Constructor Detail

MultivariateFunctionPenaltyAdapter

When the optimizer provided points are out of range, the value of the
penalty function will be used instead of the value of the underlying
function. In order for this penalty to be effective in rejecting this
point during the optimization process, the penalty function value should
be defined with care. This value is computed as:

penalty(point) = offset + ∑i[scale[i] * √|point[i]-boundary[i]|]

where indices i correspond to all the components that violates their boundaries.

So when attempting a function minimization, offset should be larger than
the maximum expected value of the underlying function and scale components
should all be positive. When attempting a function maximization, offset
should be lesser than the minimum expected value of the underlying function
and scale components should all be negative.
minimization, and lesser than the minimum expected value of the underlying
function when attempting maximization.

These choices for the penalty function have two properties. First, all out
of range points will return a function value that is worse than the value
returned by any in range point. Second, the penalty is worse for large
boundaries violation than for small violations, so the optimizer has an hint
about the direction in which it should search for acceptable points.

Parameters:

bounded - bounded function

lower - lower bounds for each element of the input parameters array
(some elements may be set to Double.NEGATIVE_INFINITY for
unbounded values)

upper - upper bounds for each element of the input parameters array
(some elements may be set to Double.POSITIVE_INFINITY for
unbounded values)

offset - base offset of the penalty function

scale - scale of the penalty function

Throws:

DimensionMismatchException - if lower bounds, upper bounds and
scales are not consistent, either according to dimension or to bounadary
values

Method Detail

value

This method simply returns the value of the underlying function
if the unbounded point already fulfills the bounds, and compute
a replacement value using the offset and scale if bounds are
violated, without calling the function at all.